Realizing both boundary gain and granular gain when quantizing data is widely recognized as being difficult to accomplish for a source with memory, in which samples output by the source are correlated rather than independent. One scheme which achieves both types of gain is described in Laroia et al., "A New Structured Quantizer for Sources With Memory," Proceedings of the International Symposium on Information Theory, San Antonio, Tex., Jan. 17-22, 1993, p. 169. This scheme first quantizes the source to a sequence of a trellis code (to realized granular gain). It then uses a memory encoder which removes the source memory and adds a dither sequence to the data so that conventional techniques for implementing codebook boundaries for the corresponding memoryless innovations source can be applied. However, because of the dither sequence, the implemented codebook boundary only approximates the desired codebook boundary for the innovations source. For low rate quantization, this approximation can lead to significant performance degradation. Moreover, since the samples of the dither sequence are contained in the Voronoi region of the final level of lattice partitioning, performance degradation depends on the number of coset partitions used to generate the trellis code that achieves the granular gain, and increases when a more powerful trellis code is used.